Biologically Related Models for
Treatment Planning
Ellen Yorke
Memorial Sloan-Kettering Cancer Center
Reference list as additional handout
• All treatment planning is biological in nature
– What is a “biological” or “biologically related” model?
• An equation or algorithm that combines
dosimetric and other factors to predict treatment
outcome
– “Other”: medical factors (type of cancer, chemo, age),
‘biological’ factors (FDG uptake, hypoxia, genomics)
– Model may be
• Descriptive (algorithmic reformulation of outcomes data)
• Mechanistic (built on physiological or cellular data)
• Are biological models more reliable predictors of
outcomes than dose/dose-volume plan features?
– Especially when applied to your patients?
• Are optimizers based on biological models better?
Better=More efficiently generated
Better=plans the MD prefers
Better= Plans with better outcomes
• Several commercial TPS have plan evaluation and
optimization modules based on biological models
– TG 166: biologically based treatment planning (BBTP)
http://www.aapm.org/pubs/reports/RPT_166.pdf
• Endpoints of successful treatment planning
– High tumor control (eradicate the irradiated tumor)
• High Tumor Control Probability (TCP)
– Low incidence of complications
• Low Normal Tissue Complication Probability (NTCP)
• This talk will discuss several popular biological models
– Generalized Equivalent Uniform Dose (gEUD)
• Optimize and evaluate dose distributions for tumors and normal
tissues
– Linear-Quadratic (LQ) Model
• Dose/fraction effects for tumors and normal tissues
– TCP models- general nature
• Predict TCP for given irradiation pattern; used for optimization and
evaluation
– NTCP models- general nature
• Predict complication rates for given irradiation pattern; used for
optimization and evaluation
gEUD (Generalized Uniform Dose)
• “The uniform dose that, if delivered over the
same number of fractions as the non-uniform
dose distribution of interest, yields the same
radiobiological effect” (TG 166, Niemierko 1999)
• gEUD= (∑vi (Di )a)1/a
• ‘a’: user-chosen parameter
D ,v
• Convenient optimization term
0.45
0.4
Fractional Volume
0.35
2
0.3
2
0.25
0.2
0.15
D1 , v 1
0.1
0.05
0
0
10
20
30
40
Dose (Gy)
50
60
70
80
gEUD dependence on “a”
0.45
a
0.4
-20
gEUD
(Gy)
34.8
0.2
49.3
1
50
20
60.9
100
67.9
Fractional Volume
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
10
20
30
40
50
60
70
80
Dose (Gy)
• a <0: cold spots dominate (use
negative a for tumors)
• a=1: gEUD= mean dose
• a large positive : hot spots
dominate (use for normal tissues
like spinal cord)
Linear-Quadratic (LQ) Model
• Observed: Same total dose delivered
at high dose/fraction is more potent
than at low dose/fraction
– SBRT (hypofractionation) vs
conventional fractionation (~ 2 Gy/fx)
• Radiobiology experiments:
Surviving fraction (SF) of cells vs
single dose D fits well to
SF=exp(-α D (1+ D/[α/β])
• α (units Gy-1 ) and β (units Gy-2 ) are
independent of D
– Depend on type of cell or organ
response and irradiation conditions
– RBE, dose rate, hypoxia
• More complex versions of LQ not
discussed here- see references
LQ Model: fractionated RT
• Dose D delivered in n fractions (d=D/n)
SF=exp(-αD (1+d/[α/β]))
• D (1+d/[α/β])=Biologically Effective Dose (BED)
• Hypothesis: Regimens with the same LQ model
BED have the same biological effect (isoeffective)
on living tissues to which they are applied
– In vitro, same BED means same SF
• D1 in fractions d1 is isoeffective to D2 in fractions d2 if
D1(1+d1/[α/β])=D2 (1+d2/[α/β])
• LQED2 = dose in 2 Gy fractions that is isoeffective to (D,d)
LQED2=D(1+d/[α/β]))/(1+2/[α/β])
0
-1
Log10 Surviving Fraction
-2
-3
-4
-5
-6
-7
-8
-9
0
4 Gy/fx
single fx
pure linear
5
Dose (Gy)
10
15
20
Log10(SF)=-αD(1+d/[α/β])
LQ model is suspect at low
(≤ 1 Gy) and high (srs, sbrt)
dose/fx
• There are other models but LQ is
most commonly used because:
• LQ fits decently over much of the
clinical dose range
• LQ is mathematically simple
Park et al, IJROBP 70
BED_V Hs
100
Physical Dose
BED_alfabeta 2_30 fractions
BED_alfabeta 10_30 fractions
BED_alfabeta 2_10 fractions
BED_alfabeta 10_10 fractions
% Volume
•For fixed D
• BED> D
•Different α/β’s
α/β , BED
BED=D (1+d/[α/β])
80
60
40
• Same α/β
•# fx , BED
because
• # fx , d
20
0
0
50
LQED2_VHs
350
Physical Dose
LQED2_alfabeta 2_30 fractions
LQED2_alfabeta 10_30 fractions
LQED2_alfabeta2_10 fractions
LQED2_alfabeta10_10 fractions
80
% Volume
• Rx/fx ~ 2 Gy,
LQED2_VH
similar to DVH
300
LQED2=BED/(1+2/[α/β])
100
• d<2, LQED2<D
100
Dose or BED (Gy)
150
200
250
60
40
20
Dose or LQED2 (Gy)
0
0
50
100
150
200
• For MV photon and electron radiation, α ranges from
~ 0.1 Gy-1 [radioresistant] to ~ 0.7 Gy-1 [radiosensitive]
• α/β ranges from ~ 1 Gy [effect depends strongly on
the dose per fraction] to 15 Gy [effect depends only
weakly on dose per fraction]
• The LQ model is semi-mechanistic; related to DNA
damage mechanisms
– Model refinements account for repair during the
delivery time and proliferation between fractions
• See Hall & Giaccia, Joiner & van der Kogel (good references and good
source of LQ parameters)
• Stay tuned for a future ICRU Report (#25) which aims to bring
order to the LQ-model terminology wilderness
Tumor Control Probability (TCP)
• Tumor control: irradiated tumor doesn’t grow after
radiation treatment course ends
• TCP is sigmoidally increasing function of dose.
• For given tumor type and irradiation conditions
– D50=dose for 50% TCP of uniformly irradiated tumors
– γ50=% ∆TCP /% ∆(d/D50) evaluated at d/D50=1
• Typical γ50 range: 1 (shallow curve) – 5 (steep curve)
100
• Many equations are used for TCP
• Some have no mechanistic basis- just
approximately right shape
• For example _ the Log Logistic
60
40
TCP(%)
80
20
TCP=100/(1+(D50/D)4γ50)
Dose/D50
0
0
0.5
1
1.5
2
Poisson-LQ cell kill TCP model
• Assume N clonogenic cells (cells that can regrow tumor)
– Assume LQ: SF=exp(- αD(1+d/[α/β])
– Assume the number of clonogens that survive treatment is
Poisson distributed
– Assume TCP=probability of no surviving clonogens
• TCP= exp(-N exp(- αD(1+d/[α/β]))
• N can be calculated from γ50; with these assumptions, N
is very small for observed γ50’s
– <~100 cells, independent of tumor size
• Two different approaches to this puzzle:
– There really are very few clonogens – just carry on
– There are many clonogens (~ 107/cc) but observed TCP is a
population average over a range of sensitivities (α’s); averaging
smears out the slope (Niemierko & Goitein 1993; Webb & Nahum, 1993)
TCP for non-uniform radiation
• Break tumor into ‘tumorlets’, each with uniform dose
– Which structure to use: PTV? CTV? GTV?
• Start from differential DVH {Di, vi}
• TCP =Πi (TCP(Di,di))vi
• This approach can model non-uniform tumor
characteristics as well as non-uniform doses
– (D50’s, clonogen densities, etc)
– Can we use information from molecular imaging?
• Location? LQ parameters? Relevant cell density?
• Dose-painting guided by PET, etc?
• For tumors, given current knowledge are fancier
models (TCP) than dose or BED/volume metrics or
gEUD with consistent ‘a’ useful for tx planning?
Normal Tissue Complication Probability
(NTCP)
100
γ50 =Normalized slope at TD50
90
Slope (Gy-1)=100 γ50/TD50 (Gy)
NTCP(%)
80
The assumed
sigmoidal shape is
rarely evidence-based
70
Most clinical data at
low NTCP
60
50
TD5: dose for 5%
complication probability
40
30
TD50: Dose for 50%
complication probability
20
10
0
20
30
40
50
60
Dose(Gy)
70
80
90
100
Complications are Complicated
• Most organs have more than one complication, each
with different dosimetric correlates
– Lung: pneumonitis, fibrosis
– Rectum: bleeding, incontinence, fistula
• Acute complications: during or soon after treatment
• Late complications: many months-years latency
• A complication can be mild, intermediate, or severe
– Toxicity grading: 1 (mild, asymptomatic) – 5 (fatal)
– CTCAE 4.03*, RTOG, SWOG
• ‘Tolerable’ complication rate depends on impact of
toxicity on quality of life and on treatment tradeoffs
– Serious risk more acceptable in last-chance scenarios
* http://evs.nci.nih.gov/ftp1/CTCAE/CTCAE_4.03_2010-06-14_QuickReference_8.5x11.pdf
NTCP: Tolerance Doses
Tolerance dose (or dose/volume metric) depends on:
• The complication
• The dose/fraction
– LQ model generally used
– Acute complications: α/β typically large (~ 10 Gy)
• Weak dependence on dose/fx
– Late complications: α/β typically small (< 5 Gy)
• Strong dependence on dose/fx
• The dose distribution
• And other things which we won’t handle here
– Dose rate (external beam vs LDR)
– Medical factors (chemo, smoking, co-morbidities)
– RBE (protons, heavy ions)
Tolerance dose-volume dependence
Partial organ irradiation (see Emami 1991)
Zero dose
Volume fraction=1-v
Uniform Dose D
Volume fraction=v
5% complication vs irradiated volume fraction
Emami, 1991
70
TD5/5 (Gy)
60
50
Severe RILD
40
Radiation Pneumonitis
30
Radiation Pericarditis
esophageal stricture
20
radiation myelitis
(reference length 20
cm)
10
0
0
20
40
60
80
% Organ Irradiated
100
120
Observed
•Iso-complication
dose increases as
irradiated volume
fraction decreases
•Weak vs strong
volume effects
Power Law ‘Fit’ to Volume Dependence
TDc vs volume fraction in
partial organ irradiation
Inverse relationship between
tolerance dose TDc% and irradiated
volume fraction, v
TDc(v)=TDc(1)/vn
Descriptive (not mechanistic)
Low n-> myelitis, brainstem necrosis
High n-> pneumonitis, xerostomia, RILD
Mid n-> rectal bleeding, pericarditis
Serial-type response
Low n-> weak volume dependence,
Dmax dominates
Parallel-type response
High n-> strong volume dependence
n=1: mean dose dependence
NTCP: Lyman Model
Most popular in USA
• Power law volume dependence
• 4 complication-specific parameters: n, TD50(1),
slope parameter m, reference volume for v=1
(D -TD50(v))/(m TD50(v))
NTCP= (2π)-1/2 ∫ exp(-t2/2)dt
-∞
• Also called Lyman-Kutcher or LKB (Lyman-Kutcher-Burman) Model
• Histogram reduction converts general DVH, {Di, vi}, to an
equivalent uniform or partial irradiation
–
Deff = (Σ vi (Di)1/n)n , v = 1 (whole organ)
• Use Deff for D and 1 for v in upper limit of integral
– or veff= Σvi (Di/Dref)1/n
• Use Veff for V and D ref for D in upper limit of integral
Lyman Model Deff is gEUD
• Lyman Deff = (∑vi (Di)1/n )n
• gEUD= (∑vi (Di)a )1/a
• a=1/n
– Serial-type response: large a, small n ( n<1)
– Parallel-type response: small a, large n (n≥1)
• There are Lyman model parameters in the
literature for many complications
– Classical: Burman et al, IJROBP 21 (1991) p 123-135
– QUANTEC: IJROBP 76. Vp; 3S (2010 )
– Watch for ongoing research
NTCP: Källman s-model (Relative seriality)
Källman et al, Int J Rad Biol 62, 249-62
• Popular in Europe – implemented on some
commercial TPS
• Organ responds to radiation damage in combined
serial and parallel fashion
• 4 parameters (and α/β if use LQ)
– D50 and γ50 for whole organ response to uniform dose
– s =‘seriality parameter’; s=1 for weak volume
dependence, small s for strong dependence
• With proper parameters, NTCP curves similar to
Lyman
• Planners routinely include volume dependences
as planning goals for many organs
– This is not new!
– Cord: Dmax<50 Gy (avoid myelitis)
– Parotid: Mean dose < 26 Gy (avoid xerostomia)
– Lung: Mean dose< 20 Gy (avoid pneumonitis)
• Where do these numbers come from?
– Literature
• Emami, QUANTEC, subsequent publications
• Red and Green Journals and meetings are good
sources of updates
Pitfalls and cautions
• To use models for plan evaluation
– Use reliable sources of parameters
• Cautiously update as knowledge evolves
– Your patients may be different so…..
– Test carefully against your clinic’s outcomes before
changing your plan acceptance criteria
• Hypofractionation is a vast unknown
– TG101 and floods of peer-reviewed literature
• To use models to drive optimization
– If you get qualitatively similar, ‘good’ plans faster with
biological optimizations, that’s great but….
– Watch out for unusual distributions
• For example, gEUD may steer hot or cold spots to odd places
• Clinical outcomes still the best criteria for ‘good’ plans
•
1.
2.
3.
General References on Biological Models
TG166 Report: http://www.aapm.org/pubs/reports/RPT_166.pdf (full report); short form in Medical Physics
(http://www.aapm.org/pubs/reports/RPT_166ShortReport.pdf)
QUANTEC supplement to Int Jnl of Radiat Oncol Biol Phys http://www.aapm.org/pubs/QUANTEC.asp
The “Emami paper” (NTCP)
1.
B. Emami, J. Lyman, A. Brown, L. Coia, M. Goitein, J. E. Munzenrider, B. Shank, L. J. Solin, and M. Wesson, “Tolerance of
normal tissue to therapeutic irradiation,” Int. J. Radiat. Oncol. Biol. Phys. 21, 109–122 (1991).
Companion paper on Lyman model: Burman C., G.J. Kutcher, B. Emami, M. Goitein. (1991). “Fitting of normal tissue tolerance
data to an analytic function.” Int J Radiat Oncol Biol Phys 21: 123-135.
2.
4.
5.
6.
7.
8.
9.
“Basic Clinical Radiobiology, 4th Edition” edited by Joiner and van der Kogel, Hodder Arnold, London (2009)
“Radiobiology for the Radiologist, 7th edition”, Hall and Giaccia, Lippincott, Williams and Wilkins, Philadelphia
(2012)
Interesting view on TCP: Zaider M and Hanin L, Tumor control probability in radiation treatment, Med Phys 38,
574-583 (2011)
Interesting view of NTCP: Trott, Doerr, Facoetti, Hopewell et al, “Biological mechanisms of normal tissue
damage: Importance for the design of NTCP models”, Radiother and Oncol in press, 2012
Normal tissue guidelines for SBRT: Table III of the report of TG 101
(http://www.aapm.org/pubs/reports/RPT_101.pdf). It is very important to note that the TG itself says “The
doses are mostly unvalidated, and while most are based on toxicity observation and theory, there is a measure
of educated guessing involved as well.”
TCP-Population averaging
1.
2.
10.
Niemierko A , Goitein M, “Implementation of a model for estimating tumor control probability for an inhomogeneously
irradiated tumor”, Radiother and Oncol 29, 140-147 (1993)
Webb S, Nahum AE “A model for calculating tumor control probability in radiotherapy including the effects of
inhomogeneous distributions of dose and clonogenic cell density”, Phys Med Biol 38, 653-66 (1993)
Brachytherapy (especially LDR brachy) is quite different and is not covered by TG166: In addition to the
radiobiology text references, look at the report of AAPM TG 137
(http://www.aapm.org/pubs/reports/RPT_137ExecSummary.pdf)
NTCP since QUANTEC
•
QUANTEC cites consensus-selected NTCP references, up to ~ 2009, covering mostly conventional
fractionation. Here are a few standard-fractionation NTCP modeling studies published since
QUANTEC that look interesting (PubMed search). Hypofractionation (sbrt) is in such vigorous flux
that I don’t dare make suggestions!
• Rectal toxicity:
1.
Guilliford SL, et al, “Parameters for the Lyman Kutcher Burman (LKB) model of Normal Tissue
Complication Probaiblity (NTCP) for specific rectal complications observed in clinical practise”,
Radiother and Oncol 102, p 347 - (2012)
2.
Prior P, Devisetty K et al, “Consolidating risk estimates for radiation-induced complications in
individual patient: late rectal toxicity”, Int J Radiat Oncol Biol Phys 83, p 53- (2012) {also has
many references to literature}
3.
Defraene G, Van Den Bergh L, et al “The benefits of including clinical factors in rectal normal
tissue complication probability modeling after radiotherapy for prostate cancer”, Int J Radiat
Oncol Biol Phys 83, p 53- (2012)
4.
Liu M, Moiseenko V, et al “Normal Tissue Complication probabioity (NTCP) modeling of late rectal
bleeding following external beam radiotherapy for prostate cancer: A test of the QUANTECrecommended NTCP model.” Acta Oncol 49, 1040-4 (2010).
• Lung toxicity:
Palma DA, Senan S et al, “Predicting radiation pneumonitis after chemoradiation therapy for lung
cancer: an international individual patient data meta-analysis.” Int J Radiat Oncol Biol Phys 2012
(check epubs)